How do I write radian decimals in terms of Pi?

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Discussion Overview

The discussion revolves around how to express the radian measure of 1.047 in terms of π. Participants explore the conversion process and the reasoning behind the calculations, focusing on the relationship between decimal radians and their equivalent fractions of π.

Discussion Character

  • Technical explanation, Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant asks how to express 1.047 radians in terms of π, noting they believe the answer is π/3 but seek clarification on the conversion process.
  • Another participant provides a calculation showing that 1.047 divided by π is approximately 1/3, leading to the conclusion that 1.047 radians equals π/3.
  • A subsequent reply questions the approximation used, noting that calculating 1.047 / π yields a value of 0.33327, which raises confusion about the earlier approximation of 1/3.
  • Another participant suggests that since 1.047 has four significant figures, the conversion should reflect that, proposing a value of x as 3.001 when relating it back to π.

Areas of Agreement / Disagreement

Participants express differing views on the approximation of 1.047 / π, with some accepting the approximation while others challenge its accuracy. The discussion remains unresolved regarding the exactness of the conversion.

Contextual Notes

There is a lack of consensus on the method of approximation and the significance of significant figures in the conversion process. The discussion does not clarify the assumptions behind the approximations used.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the conversion of radian measures to expressions involving π, particularly in contexts where precision and significant figures are important.

jester0608
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How would i write 1.047 rad in terms of pi? I know the answer i will get is Pi/3 rad, but HOW do i get this answer? I know how to convert degrees to radians and vice versa in terms of pi but this particular question is in radians. Help?
 
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1.047/pi≈1/3
1/3*pi=pi/3
 
n_kelthuzad said:
1.047/pi≈1/3
1/3*pi=pi/3

But when I calculate 1.047 / pi I get 0.33327. How did you get 1.047/pi ≈ 1/3 ? that's the only part i don't understand
 
Since your result 1.047 is written with 4 significant figures, you ought to keep that many in \theta = \pi / x \Rightarrow x =\pi / \theta = 3.001.
 

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